The Book - Rice University

The Book

The Man

May 14, 2006

Chapter 1

Opportunism in Wireless Networks:

Principles and Techniques

Ahmad Khoshnevis and Ashutosh Sabharwal1

1.1 Opportunism: Avenues and Basic Principles

In this chapter, we will study how the variation in the sources and channels can be exploited

to improve the power and spectral efficiency of wireless networks. A typical multi-hop wire-

less network is displayed in Figure 1.1, with an inside look into a typical node. At any node,

there can be multiple sources with multiple queues, either based on the data generated at

the node (a user web-surfing) or generated at other nodes (forwarding traffic in a multi-hop

network like ad hoc, sensor or mesh network). Most sources produce information in time-

varying bursts. This is clearly evident in multimedia sources like voice, music and video,

which when compressed yield a time-varying amount of information. Voice conversations

have periods of silence and speech interspersed, clearly de-marking periods of high informa-

1Department of Electrical and Computer Engineering, Rice University, Houston, TX 77005, USA. Email:{farbod,ashu}@rice.edu. Phone: (713) 348-5057. Fax: (713) 348-6196.

1

2CHAPTER 1. OPPORTUNISM IN WIRELESS NETWORKS: PRINCIPLES AND TECHNIQUES

Transmitter

Multiple Antennas

Multiple time-varyinginput sources

Multiple Access

Time-varying wireless channels

A

B

E

D

C

F

Figure 1.1: A typical multi-hop wireless network with multiple nodes. The figure also showsan expanded view of a typical node which could have multiple sources to be sent using aphysical layer transmission over multiple antennas.

tion followed by low-information segments. The same time-varying burstiness is evident in

a multi-tude of data sources ranging from web browsing to sensing natural scenery in sensor

networks. In fact, the traffic in many networks is bursty at multiple time-scales, evident from

abundance of self-similar traffic models studied in wireline [40, 6] and wireless networks [22].

Time-varying data rates of source implies a time-varying demand.

Analogous to time-varying sources is the well-known property of wireless channels, whose

quality vary over time. The time-varying nature of the wireless channels can be attributed to

mobility of users and their surrounding environment. Electromagnetic signals transmitted by

base-station or mobile users reach the intended receiver via several paths; the multiple paths

are caused by reflections from man-made and natural objects. Since the length of the each

path may be different, the resultant received signal shows a wide fluctuations in its power

profile, thereby complicating the design of spectrally efficient systems. If the transmitter

and/or receiver is equipped with multiple antennas, then between any two nodes, there are a

1.1. OPPORTUNISM: AVENUES AND BASIC PRINCIPLES 3

multiple wireless channels which may vary independent of each other depending on antenna

configuration. This time-variability implies that channels have a data capacity which varies

with time.

Thus, a typical wireless network consists of time-varying

demand (sources) and time-varying capacity (channels).

In this chapter, our goal will be to study techniques which exploit the inherent time-

variability in networks to improve performance. Grouped together under the broad class

of called opportunistic techniques, the aim is to conserve resource under poor channel con-

dition (or high source demand) and judiciously use them in favorable conditions.

1.1.1 Degrees of Freedom

Performance of communication over wireless links can be characterized by the number of

independent degrees of freedom along which a radio signal can be transmitted. The sta-

tistical degrees of freedom, available in spectral, temporal and spatial domain describe the

dimensions available to send a wireless signal.

Temporal and Spectral Dimensions: Consider any signal, X(t), which is transmitted

over a bandwidth of W Hz for time duration of T seconds. It is well-known from [34]

that any such signal has ∼ 2WT signaling dimensions. That is, only 2WT independent

parameters are available at the transmitter to control the type of the signal which can be

transmitted over the channel. Note that these dimensions are not statistical in form, i.e, they

are available for any transmission as long as it is band- and time-limited. After transmission

through the wireless channel, the signal undergoes distortions due to multi-path propagation

between the transmitter and the receiver. The number of dimensions which determine the

communication system performance are the ones observable at the receiver. Thus, if some of

the dimensions are lost during the transmission due to poor channel conditions, the effective

number of dimensions available for communication are less than 2WT . Since the channel

variations are best characterized statistically due to random fluctuations of the channel gain

and phases, the receive degrees of freedom are also best characterized statistically.


Spatial Dimensions: The 2WT formula gives the number of spectro-temporal dimensions

for single antenna transmitter and receiver pair. In wireless systems, spatial variations can

also be exploited by the use of multiple transmit and receive antennas. For rich scattering

environments, like those encountered in indoor channels or when then transmitter and re-

ceiver are located at low heights (potentially in dense deployments of sensor networks), each

additional transmit-receive pair adds a new dimension. Thus, in a multiple antenna system

with n transmit and n receive antennas, we have 2nWT dimensions for signaling [35, 37].

Spatial degrees of freedom are also available in multiple user systems. Due to differences in

topological environment, the propagation environment between any transmitter and receiver

is different between any other transmitter-receiver pair. Consider node A in Figure 1.1 which

is communicating with three nodes (B, C and D). The three channels, A–B, A–C and A–D

vary independent of each other and thus have the same characteristics as a multiple antenna

system.

Source “Degrees of Freedom”: In general, sources are not characterized in the same

framework as the channels. However, there is certain “duality” between sources and channels,

which allows a conceptual interpretation of many source opportunism based techniques as

duals of channel opportunism based methods. For example, any arrival process A(t)can be

characterized by its temporal properties and spectrum, since it is simply a time-series like a

channel H(t) or the transmitted signal X(t). Similarly, there can be multiple independent

sources at any node (as shown in Figure 1.1), which are analogous to multiple independent

channels like in multiple antenna links between two nodes.

However, there are some fundamental differences between sources and channels depending

on the network usage. While the channel between any two nodes (as long they are reasonably

far away from each other) varies independent of the channel between any two other nodes,

the sources at each node can be strongly correlated across nodes. For example in Figure 1.1,

the data at node D travels to F via node E, which implies that there is a potential for

correlation between the arrival process at nodes D, E and F. The only reason these arrival

processes may not be perfectly correlated is due to random departures from each node due

to channel time-variations. Thus, the random nature of transmissions can “de-correlate” the

1.1. OPPORTUNISM: AVENUES AND BASIC PRINCIPLES 5

arrival process across multiple nodes [30].

1.1.2 Roadmap

The general principle behind all opportunistic methods is to adapt transmitter

actions based on the current conditions of the source and the channel.

For example, source burstiness has been conventionally exploited in communication networks

via statistical multiplexing them over the same link using random access methods [1]; statis-

tical multiplexing automatically provides more bandwidth to the user which has high current

data need. To understand the basic principles, we will study simple bare-bones formulations

in depth and then apply the lessons learnt to real networks. We will follow a rigorous ap-

proach to the derivation, all of them inspired by the information-theoretic method. The

outline for the rest of the chapter and major milestones are as follows.

Source Opportunism: Focusing on a single point-to-point link, we will first study (Sec-

tion 1.2) how scheduling packets from a bursty source can be used to reduce the power

consumption of any node. The opportunism can be attributed to allowing more delay in the

system to avoid sending large bursts of packets in any single transmission slot.

Temporal-spatial opportunism over a single link: Our next focus will multiple antenna

links and how temporal and spatial degrees of freedom can be exploited in opportunistic

manner (Section 1.3). The key concepts that if the transmitter can receive information (even

if a few quantized bits [18]) about the channel conditions, then it can adapt its physical layer

parameters like modulation, code rate and power to optimally use the channel conditions.

Physical adaptation is commonly used in many current wireless networks (cellular networks

like IS-95, 3G) and is proposed in upcoming standards (like IEEE 802.11n).

Temporal-spatial opportunism in ad hoc networks: The adaptive physical layer con-

cepts are next applied to ad hoc networks, to allow opportunistic tuning of transmission rate

(Section 1.4). Using the framework of IEEE 802.11 4-way handshake (RTS-CTS-DATA-

ACK), we discuss Opportunistic Auto-Rate MAC protocol (OAR) that performs per packet


rate adaptation to significantly improve the throughput compared to current systems.

Temporal-spectral-spatial opportunism in ad hoc networks: Finally, we show (Sec-

tion 1.5) how all three dimensions can be fruit-fully exploited to further increase the capacity

of OAR protocol by a multi-channel adaptation labeled Multichannel OAR (MOAR).

1.2 Source Opportunism

1.2.1 Problem Formulation

Consider a time-slotted system, each Ts seconds long, with an input buffer to queue arriving

packets. In time slot n, there are an arriving packets, each of which is assumed to have same

number of information bits. The simplest source model assumes independent and identically

distributed (i.i.d.) arrival from one time-slot to another, according to the distribution p(an).

In more complex and realistic models, the arriving packets an can be correlated over time,

such as signals generated by measurements of a thermometer. Though correlated models

are important for practical systems, the key issue which affects the performance of the

system is whether the scheduler at the transmitter has knowledge of the distribution of the

arrival process or not. Thus, our problem formulations and the subsequent development in

this section will explore how scheduler structure differs with and without the knowledge of

source statistics.

Every time slot dn packets are appropriately modulated as Xn and transmitted over an

additive white Gaussian noise wireless channel, given by

Yn =√

PnXn + εn. (1.1)

Thus, each transmission packet Xn is unit power and power Pn is the power at which the

packet is transmitted in slot n. Further the additive white Gaussian noise component, εn

is assumed to be zero mean and unit variance. With the above setup, the queue evolves

1.2. SOURCE OPPORTUNISM 7

according to the following equation,

xn+1 = max(xn + an − dn, 0). (1.2)

The transmission√

PnXn has to be designed such that the receiver can decode the packets

reliably. We will use an information-theoretic notion of reliability, motivated by [28]. To

invoke mutual information based reliability, we require that the time slot duration, Ts, be

long enough to encode dn packets close to channel capacity. More precisely, rate at which

dn packets can be reliably decoded when sent in a fixed length Ts time-slot is given by

dn = log (1 + Pn) , (1.3)

where, for simplicity, we have assumed that the system bandwidth is 1 Hz. Equivalently, the

power required to ensure reliable reception is given by

Pn = edn − 1. (1.4)

The relation between the number of scheduled packets dn and the power required for their

transmission shows that a linear increase in number of scheduled packets requires exponential

increases in transmit power. The above convex relation between dn and Pn will also be the

reason why power control is important even without any channel variations.

Our objective is to minimize the average transmit power consumption of the transmitter

such that the packet delay does not exceed an average or a maximum delay bound,

P ∗(D0) = minΘ(D0)

limn→∞

E {Pn} (1.5)

The set of schedulers Θ(D0) consists of all those schedulers which (a) do not drop any

packets and (b) ensure that the queueing delay is no more than D0, which may be measured

on average or as the maximum packet delay. We will consider two important classes of

schedulers. In the first class, the scheduler completely knows the packet arrival distribution

and hence formulates its scheduling decisions based on source statistics. In contrast, the

second class of schedulers work without any knowledge of the source statistics and hence


aim to be perform only based on current arrivals without utilizing arrival distributions.

1.2.2 Fully Informed Schedulers

In this section, we will study the tradeoff between the average transmit power and the result-

ing average queuing delay of optimal schedulers. Our approach will be to first (a) characterize

the nature of schedulers which achieve the minimum in optimization criterion (1.5), (b) study

the nature of optimal schedulers to derive sub-optimal, computationally simple schedulers

and lastly (c) derive an intuitive analytical approximation for the relation between average

power and average queuing delay of optimal schedulers.

A scheduler is a mapping from the queue state (xn) to the number of packet departures

(dn). Given the number of scheduled departures, the packet encoding and corresponding

power Pn is decided by the physical using the Equation (1.4). We will consider both the set of

randomized schedulers, S = {α|α : xn 7→ dn}, where a general scheduler mapping is defined

by probabilities αj,i = Prob(dn = j|xn = i). Since αj,i are probabilities,∑i

j=0 αj,i = 1. The

set of valid schedulers is thus all those probabilities which satisfy the above properties. A

scheduler is called a deterministic if αj,i ∈ {0, 1}.

The two key metrics of interest are average queuing delay and average power of the

scheduler, which we will denote by Davg(α) and Pavg(α). The work in [29] characterizes the

subset of schedulers Θ ⊂ S which do not lose any packet (no packet dropped at transmitter

and enough power used for receiver to ensure reliable decoding). Furthermore, it is shown

that the delay and power of any zero-outage randomized scheduler can be expressed as a

convex combination of delay and power of deterministic zero-outage schedulers, as described

by the following result.

Theorem 1 (Characterization of delay and power) Consider a queue with finite buffer

size L and an input process with no more than M packet arrivals in one slot. Define W as

the set of deterministic schedulers. Then, for any randomized scheduler φ ∈ Θ, there exists


η′i ∈ [0, 1], i = 1, 2, . . . , F ′ = |W ∩Θ|, with

F ′∑i=1

η′i = 1, such that

Davg(φ) =F ′∑i=1

η′

iDavg(γi) (1.6)

Pavg(φ) =F ′∑i=1

η′

iPavg(γi), (1.7)

where γi is a scheduler and γi ∈ W ∩ Θ for all i. Finally, the boundary of the achievable

region in the delay-power plane is piecewise linear with the vertices achieved by deterministic

schedulers.

Thus the average packet delay achieved by any zero outage randomized scheduler is given

by a convex combination of the average packet delays achieved by all possible zero outage

deterministic schedulers. In addition, the same convex combination of the average powers of

the zero outage deterministic schedulers gives the average power of zero outage randomized

policy.

To compute the optimal scheduler (randomized) for a desired delay bound Davg, dynamic

programming based technique commonly known as value iteration algorithm (VIA) [32] can

be employed. For large values of buffer sizes, L, the number of states in the VIA increase

exponentially and hence computing the optimal scheduler is computationally intensive. For

the cases where the arrival distribution is measured in real-time and the optimal scheduler

is adapted over time, the implementation of VIA can lead to an intractable design. There

are two possible techniques to reduce the computational complexity of scheduler design.

A simple method for complexity reduction is to reduce the number of states in the VIA.

The following state reduction is most useful for moderate to large delay scenarios. As

delay increases beyond 1 time-slot, the scheduler tends to take the same action in several

consecutive queue states. Thus, to reduce the state diagram size, multiple states can be

morphed into one state. For instance, for all states xn = j, . . . , j + K, the scheduler can be

constrained to take the same action un, thereby reducing the state space. It is clear that

the constrained system will be suboptimal, but the loss due to additional constraints can be


minimized by appropriate choice of the number and lengths of constraint intervals.

The second suboptimal scheduler is labeled the log-linear scheduler, described as follows.

For a queuing delay of one time-slot the optimal scheduler flushes the buffer at all time-

slots, i.e., dn = xn and the corresponding power required in each time-slot is proportional

to edn(xn). As the delay increases, we observe that the optimal scheduler tends to choose

dn(xn) so that the power in each time-slot is linearly proportional to xn, thereby “equalizing”

the power penalty in large buffer states xn. For equalizing the power, the scheduler picks

packets dn(xn) ≈ log(xn). Combined with the natural constraint that we cannot transmit

more packets than available (un ≤ xn), we propose the following log-linear scheduler,

un = min (xn, blog(κxn)c) . (1.8)

The parameter κ of the log-linear scheduler is chosen to meet the delay bound. For buffer

states greater than L−M , the log-linear scheduler transmits at least xn−(L−M) packets to

prevent buffer overflows. The log-linear scheduler greatly simplifies scheduler design since it

requires only one parameter κ. The value of κ to achieve a certain average delay depends on

the arrival distribution of the source. The following straightforward adaptive algorithm can

be used to compute the value of κ dynamically to achieve any given average delay constraint

based only on the knowledge of the mean arrival rate. In the adaptive scheduler, κn is a

function of time and is updated in every time-slot as given below.

κn = κn−1 + ∆κ

(Dn −D0

), (1.9)

where Dn is the sample average delay given by the ratio of the sample average buffer length

and arrival rate. The performance of the adaptive scheduler is shown to numerically converge

to the performance of a log-linear scheduler that has full knowledge of arrival statistics [29].

Figure 1.2 compares the performance of the log-linear and the adaptive log-linear scheduler

with that of the optimal scheduler, and shows that the suboptimal methods perform very

well.

In [29], a approximate relation between average power and average queuing delay is also


1 2 3 4 5 6 75

5.5

6

6.5

7

7.5

8

8.5

9

AVER

AGE

POW

ER

AVERAGE DELAY BOUND

OPTIMALLOG!LINEARADAPTIVE LOG!LINEAR

Figure 1.2: Comparison of log-linear and adaptive log-linear schedulers with correspond-ing optimal scheduler (Buffer length L = 50, maximum arrival M = 6, uniform arrivaldistribution).

derived for the optimal scheduler as

log

(1 +

Pav

σ2

)≈ λ +

σ2a

4λDavg

(1.10)

where Pav is the average transmit power and Davg is the average queuing delay. Further λ

is the average arrival rate and σ2a is the variance of the arrival process {an}. Thus, we can

see that as the delay increases, the average transmit power decreases. Furthermore, if the

traffic is more bursty, σ2a, the gains from larger delay are also larger.

Additional queuing delay allows the scheduler to smoothen the incoming traffic,

thereby removing large swings in power requirements needed if very bursty traffic

is transmitted with low delays.

Thus, a scheduler acts as“filter” on the incoming packet arrivals, where the bandwidth of

the filter is determined by the ratio of burstiness of the traffic to average delay. In the next

section, we will further strengthen this filtering intuition and show that it is in fact provably


true that power-minimizing schedulers are in fact always low-pass filters.

1.2.3 Uninformed Robust Schedulers

In this section, we consider the problem of minimizing average transmit power with a con-

straint on maximum delay which any packet can tolerate. Let Dmax denote the maximum

delay constraint, then the following result can be proven.

Theorem 2 (Filter Characterization[16]) A scheduler which guarantees the maximum

delay Dmax for any arrived packet is a linear time variant filter of size Dmax denoted by

un = βn0 xn + βn

1 xn−1 + · · ·+ βnDmax−1xt−Dmax+1, (1.11)

where the filter coefficients satisfy the following

Dmax−1∑i=1

βn+ii = 1,∀n, (1.12)

0 ≤ βni ≤ 1,∀n, i. (1.13)

Furthermore, any time variant filter of size Dmax which satisfies the above constraints is a

valid scheduler which guarantees the maximum delay of Dmax for any packet.

Theorem 2 turns the design of the guaranteed maximum delay scheduler into the problem of

filter design with a linear structure. Therefore, we foresee the vast literature on linear filtering

theory as a fundamental tool in designing power-efficient schedulers [9, 26]. Following result

follows directly from basic filtering theory.

Corollary 3 Every feasible time-invariant scheduler is a low-pass filter.

For power-efficiency, additional delay helps by smoothening the input arrival process via

queuing [29]. It is clear that by increasing the number of filter taps (equivalently increas-

ing maximum possible scheduling delay), one can design better low-pass filters, leading to


transmit power reduction.

The intuition behind the fact that the optimal average power scheduler would have

smoother output sequence than the input sequence comes from the convexity of the

objective function of the optimization problem in (1.5).

We first present upper and lower bounds on the performance of optimal schedulers, which

will serve as benchmarks for the performance of the following scheduler designs.

Theorem 4 The average power of the optimal schedulers can be bounded as

El+1[2

al+Dmax

]≤ Pavg ≤ EDmax

[2

aDmax

](1.14)

where the input arrival rates are i.i.d. random variables with distribution fA(a) and l is any

positive number. The lower bound is tight when Dmax = 1 and the two bounds converge as

Dmax →∞.

The filter design interpretation immediately allows us to design schedulers using filtering

principles. The first such concept is that linear time-invariant filters, which leads to the ques-

tion of designing optimal time-invariant scheduler (recall optimal schedulers are potentially

time-varying filters, as shown in Theorem 2). It turns out that the optimal time-invariant

scheduler is independent of input arrival distribution and in fact, a simple moving average

filter.

Theorem 5 (Optimal time-invariant scheduler [16]) The optimal time-invariant sched-

uler has the following form,

un =xn + xn−1 + ·+ xn−Dmax+1

Dmax

(1.15)

The performance of the optimal time-invariant scheduler in Theorem 5 is given by the upper

bound in Theorem 4. In general, time-vaying schedulers perform much better. The next


result derives a time-varying scheduler, adapts the coefficients βni based on the current queue

conditions to achieve improved performance.

Theorem 6 At any given time slot n, let (Sn0 , Sn

1 , . . . , SnDmax−1) denote the vector of the

scheduled output service rates out of the queue from the previous time slot n − 1, and let

an be the new arrival which needs to be scheduled. The optimal output service rate for

the current time n, dn and the new vector of the scheduled service rate for time n + 1,

(Sn+10 , Sn+1

1 , . . . , Sn+1Dmax−1), are determined by the water-filling solution as

dn = (µ− Sn0 )+ (1.16)

Sn+1i = (µ− Sn

i+1)+∀0 ≤ i ≤ Dmax − 2 (1.17)

Sn+1Dmax−1 = 0 (1.18)

dn +Dmax−1∑

i=0

= xn (1.19)

Therefore the coefficients of the optimal robust time-varying scheduler are given by

βni =

(µ− Sni+1)

xn

,∀0 ≤ i ≤ Dmax − 1 (1.20)

The above discussion provides an extremely simple solution to the problem of robust

scheduling for delay constrained inputs to a queue. There are some important observations

which come out of above solution. First, to find the optimal robust scheduler in Theorem 6,

even though we did not use the filtering property of the scheduler, the optimal solution

turns of to be exactly a linear time-variant filter of size Dmax, which is not surprising due

to the Theorem 2. Second, the optimal values of filter coefficient are exactly function of the

past Dmax − 2 values of the input arrivals and the queue backlog, which is expected as we

discussed earlier. Third, as we mentioned earlier, the optimal scheduler intuitively should

try to make the output service rate as smooth as possible, which corresponds to the low-pass

property of the scheduler. Indeed, the water filling solution is the best verification of this

intuition. Fourth, the water-filling solution (shown in Figure 1.3) reveal that the optimal

1.3. SPATIO-TEMPORAL OPPORTUNISM OVER A SINGLE LINK 15

n-1 n n+

1

Successive water-filling at time`n-1’

n n+1 n+2

Successive Water-filling

at time`n’

Output rate

Time

Figure 1.3: Water-filling solution for the time slot n− 1 and subsequent time slot n.

solution always tries to push the scheduled time of the packets as far as possible and near

the maximum value of the tolerable delay. Finally, Figure 1.4 shows the performance of the

water-filling scheduler as compared to the upper and lower bounds.

1.3 Spatio-Temporal Opportunism Over a Single Link

Much like source variations can be exploited to improve the performance of the wireless

systems, channel time-variations can also be productively used. Time-variations occurs in

all degrees of freedom due to physical mobility of users and their surroundings, resulting in

channel conditions changing with time, frequency and space. In this section, we will explore

the fundamental ideas in exploiting channel variations for improved performance.


0 2 4 6 8 10 12 14 16 18 2010 010 110 210 310 410 510 610 710 810 9

Maximum Delay D max

Average Power vs. Delay for the Bernoulli Input

Upper-bound

Lower-bound (Jensen’s)

Water-filling

Bounds of Theorem 4 Increasing l

Figure 1.4: Performance of the optimal time-varying robust scheduler and the bounds onperformance. Note that performance of the optimal time-invariant robust scheduler matchesthe upper bound.


1.3.1 Channel Models and Problem Formulation

In a traditional system representation, as depicted in Figure 1.5, a communication channel

can be described by its transfer function H(n). If the timescale of channel variation is much

+H(n)S(n)

W(n)

Y(n)

Figure 1.5: System representation of a communication channel.

larger than the duration needed for transmission of a packet, then H(n) can be modeled sim-

ply by a complex-valued multiplicative factor known as channel coefficient. Such a channel

is referred to as flat fading channel. Wireless systems with high data rate (in order of mega

bits per second) and low mobility, such as indoor wireless LAN, wired line, and line-of-sight

wireless links are examples of flat fading channel. The input-output relation of such system

can be expressed by

Y (n) = H(n)S(n) + W (n), (1.21)

where H(n) is modeled by a random process. Distribution of H(n) highly depends on the

physical characteristic of the transmission path between the transmitter and the receiver

and objects surrounding the antennas at both ends. In an environment with large number of

scatterer (e.g. trees or furniture), H(n) can be well approximated by a zero-mean complex

Gaussian random process. Note that if we use an N ×M matrix instead of a scalar for H(n)

in (1.21) and modify the input signal ,S(n), and additive noise, W (n) to M × 1 vectors then

(1.21) represents a multiple antenna system with M transmit and N receive antennas.

The capacity, or equivalently the maximum achievable data rate with arbitrarily small

reliability, is the time average of the maximum achievable data rate at each time. The

maximum achievable data rate at each time instance, n, is given by the maximum mutual

information expression [35]

I(S(n); Y (n)) = log det(I + H(n)Q(n)H†(n)

), (1.22)


where Q(n) = E[S(n)S†(n)], and † is the complex conjugate transpose operation. Note that

for a single antenna system where S(n) is a scalar, Q(n) is the total power of the input signal

at time n. Similarly for a multiple antenna system the diagonal elements of Q(n) are the

average power on each antenna. Therefore, the total power spent at time n can be expressed

by the sum of the diagonal elements (power on each antenna) of Q(n), or more precisely

P (n) = tr{Q(n)},

and the average power is given by simply a time average of the power dissipated at each

time slot. That is

Pav = limT→∞

1

T

T∑n=1

P (n)

(a)= E[P (H)], (1.23)

where (a) is the consequence of the law of large numbers, and expectation in (a) is taken over

the distribution of H. In general the input signal can be decomposed into a power control

factor and a fixed codebook, i.e.,

S(n) = P (n)x(n),

where P (n) is the temporal adaptation scheme which controls the power and phase of the

input signal, and the input x(n) is independent of channel condition with a unit average

power E[xx†] = 1. Note that in (1.23), P (n) is replaced by P (H), which indicates the power

allocated for each realization of channel and does not concern any specific time slot, whereas

P (n) indicates the power allocated at time n. Hence, both P (n) and P (H) represent the

same quantity from different view.

When transmitter does not have any information about the channel, H, the best unbiased

strategy is to divide the power equally among all antennas, and allocate the same amount

of power at any given time instance. That is to say for any given time slot n, the allocated

power is Pav, and the power allocated to each transmit antenna is Pav/M (M is the number of

transmit antennas). But when channel state information is available at the transmitter, the


allocated power can be adjusted such that it matches the channel condition. Therefore, at

any time slot, n, the total power allocated will be a function of the channel realization at that

time slot, H(n), and the way the power is divided among transmit antennas is determined

by power control algorithm. This will be discussed in more detail in next section.

The mutual information expression in (1.22) is the maximum achievable data rate at each

time instance and because of H(n) it is a time varying quantity. To find the capacity of the

communication link it is enough to find the time average of expression (1.22), i.e.,

C(Pav) = limT→∞

1

T

T∑n=1

I(S(n); Y (n))

= limT→∞

1

T

T∑n=1

log det(I + H(n)Q(n)H†(n)

)= E

[log det

(I + HQH†)] . (1.24)

The capacity of a communication system is solution of an optimization problem with a set

of constraints. The solution as expected depends on the constraint set. What is described

above is the capacity of a communication link with average power constraint. Interested

readers can look at [5] for a complete treatment of the subject.

In design of a communication system two common schemes have been adopted by the

system engineers. One scheme is based on achieving the highest possible net throughput.

That is to get as close as possible to the upper limit defined by (1.24). The performance

metric used to evaluate different architectures and methods in this category is referred to as

the ergodic capacity or average capacity given by expression (1.24).

Second scheme, considers a fixed transmission rate, R. However, the capacity of the

channel (expression (1.22) is time varying and it may not be able to support transmission

rate R at all times. The duration of time that the instantaneous capacity of the channel is

smaller than the transmission rate, reliable communication is not possible, and transmission

is said to be in outage. So the design issue is to pick the best rate R such that the net

throughput of the system is maximized, or for any arbitrary rate R, find the adaptation

schemes that minimizes the outage. We will not discuss this scheme, however, interested


readers are referred to [3, 18]. Before delving into opportunistic resource allocation for

maximizing throughput, we shall analyze the multiple antenna system in order to extract

the important characteristics of channel matrix H(n).

1.3.2 Multiple Antenna Representation

To this point we have not discussed the differences of a multiple antenna system with a single

antenna. Consider the system model given in (1.21). Assume a multiple antenna system in

which H(n) is an N by M matrix. Applying singular value decomposition to H(n) we can

replace H(n) by its SVD equivalent to get

Y (n) = U(n)D(n)V †(n)S(n) + W (n)

Y (n) = D(n)V †(n)S(n) + W (n), (1.25)

where U and V are unitary matrices, and D is a diagonal m×m matrix with m = min(N, M).

The second equality in (1.25) is obtained by multiplying both sides of the first equation with

U †. This operation is possible when receiver has a perfect knowledge of H, which is the case

by the channel estimate unit at the receiver and training signals in the form of preambles

in most of the current systems. The diagonal elements of D are denoted by λ1/2i , where λi’s

are the eigenvalues of HH† when N < M or H†H when N ≤ M . Expanding (1.25) we get

y1(n) = λ1/21 (n)s1(n) + w1(n)

y1(n) = λ1/21 (n)s1(n) + w1(n)

...

ym(n) = λ1/2m (n)sm(n) + wm(n),

where si(n) is the ith element of V †(n)S(n). The multiple antenna system with M transmit

and N receive antennas resemble m (m = min(M, N)) independent single antenna channel.


These m virtual independent channels add new degrees of freedom

(in addition to time and frequency) to the wireless system and are

are labeled as spatial degrees of freedom.

Note that the m channels vary independent of each other, thus increasing the probability that

one or several of them are in good condition (compared to a single-antenna system), thereby

creating more opportunities for transmitter adaptation. For example, the m channels can

be used independently to increase the net throughput. In this case if the net throughput of

a single antenna system is denoted by C1(Pav), the net throughput of the multiple antenna

system can be at most as high as mC1(Pav). Alternately, the m channels can be used to

add redundancy and improve the error performance of the system. In the next section we

explain in more detail different ways that the spatial degrees of freedom can be used and

how its application may affect the net throughput.

1.3.3 Throughput Maximizing Resource Allocation

The problem of optimum power control for single and multiple antenna system is posed

rigorously and solved in [10, 14]. We state the problem and its solution briefly and explain the

physical interpretation of the result. The optimum signaling that maximizes the throughput

of a multiple antenna communication system is the solution to the following optimization

problem

min(P (n),X(n))

I(S(n), Y (n)|H(n))

Subject to: E[P (H)] ≤ P0.

The solution of the above optimization problem is known as matrix-water-filling given by

Pi,i(H)

P0/m=

1γ0− 1

γλiif λi > γ0

0, otherwise(1.26)


where γ = P0/mN0, N0 is the variance of the noise W (n) and the γ0 is the solution to power

constraint

E[Pi,i(H)] =P0

m, (1.27)

that is the average power allocated to any given eigenvalue over the long run should be the

same and equal to 1/m of the total power P0. For example a single antenna system the power

allocation is depicted in figure 1.6. The transmitter and receiver have perfect information

Channel coefficient, |H|2

Pow

er

Channel coefficient, |H|2

Rat

e

γ0 γ

0

Figure 1.6: Power and rate adaptation based on channel condition for maximizing through-put.

about the channel state H. Transmitter adjust the transmission power and rate according

to the power and rate expressions given in (1.26) and (1.22) respectively. The only practical

issue of such system is due to the variable transmission rate. It requires a large storage

capacity at the transmitter to hold different codebook for adjusting the rate and a complex

receiver capable of decoding codes of variable rate.

The channel dependent power allocation across the m spatial degrees of freedom,

Pi,i(H) is an example of spatio-temporal opportunistic technique . The power al-

location puts more power on those spatial channels which are in good condition

and puts less in poor condition. Thus, the optimization is performed in both the

dimension of antennas and time.

The information at the transmitter is normally provided by the receiver through a feedback

channel. To feedback the channel state information perfectly requires infinite amount of

1.4. SPATIO-TEMPORAL OPPORTUNISM IN AD HOC NETWORKS 23

information to be fedback (a real number or matrix is represented with infinite number

of bits). A more realistic scenario is to consider only a few amount of bits is available to

feedback information to the transmitter. In this case the receiver quantizes the channel state

and send back the quantized value using finite number of bits. The transmitter then uses

a power and rate which is a quantized version of power and rate as shown in figure 1.6. A

more complete treatment of the quantized power and rate allocation can be found in [23].

Spatial opportunism in some multiuser systems (multipoint-to-point or point-to-multipoint,

like those in cellular systems) have also been studied [20, 38] and implemented in some prac-

tical systems like Qualcomm HDR [13]. The strategy there is similar to the above methods

with m independent basestation to mobile user links replacing the m virtual channels in

multiple antenna systems. The optimal method turns out to choose a single node which

has the highest channel gain, SNRi to allow sending at the highest possible data rate,

log(1 + SNRi). The resulting use of multiple independent channels is also labeled multi-

user diversity to emphasize that the multiple spatial channels are due to multiple nodes in

the system. Mutli-user diversity systems are only proportionally fair, implying that their

short-term fairness properties can be very poor leading to large delays in the systems.

Thus, performance improvement in channel condition based adaptation inherently

introduce more delay in the transmission , much like packet scheduling to reduce

transmission power.

1.4 Spatio-Temporal Opportunism in Ad hoc Networks

In this section we introduce a modification, Opportunistic Auto Rate (OAR), to the existing

IEEE 802.11x protocol. The key idea of OAR is to opportunistically exploit high quality

channels when they occur via transmission of multiple back-to-back packets. Consequently,

nodes transmit more packets under high quality channels than under low quality channels.

In order to be able to explain the OAR mechanism, we shall briefly describe the underlying

IEEE 802.11 protocol.


1.4.1 Review of IEEE 802.11

As described in [27], IEEE 802.11 media access is based on the RTS/CTS mechanism [2].

In particular, a transmitting node must first sense an idle channel for a time period of

Distributed InterFrame Spacing (DIFS) after which it generates a random backoff timer

chosen uniformly from the range [0, w− 1], where w is referred to as the contention window.

At the first transmission attempt, w is set to CWmin (minimum contention window). After

the backoff timer reaches 0, the node transmits a short request-to-send (RTS) message.

If successfully received, the receiving node responds with a clear-to-send (CTS) message.

Any other node which hears either the RTS or CTS packet uses the data packet length

information to update its Network Allocation Vector (NAV) containing the information of

the period for which the channel will remain busy. Thus, all nodes including hidden node can

defer transmission suitably to avoid collision. Finally, a binary exponential backoff scheme

is used such that after each unsuccessful transmission, the value of w is doubled, up to the

maximum value 2mCWmin, where m is the number of unsuccessful transmission attempts.

1.4.2 Multi-rate IEEE 802.11

The physical-layers in IEEE 802.11a/b/g/n protocols are designed to have multi-rate trans-

mission capabilities. So in good channel condition the transmitter can send data at a rate

greater than the base rate (i.e., 2 Mbps in IEEE 802.11b, which is the protocol we will focus

in our discussion). Figure 1.7 shows a sample channel variation with time for a mobile speed

of 2.5 m/s. The received power shows wide fluctuations such that the supported data rate

varies between 5.5 and 2 Mbps with almost equal probability. In practice, depending on

the existence and strength of a line-of-sight path and the distance from the transmitter, the

rates that channel can support may vary within the entire range of the lowest to highest

possible data rate (the highest available rate in IEEE 802.11a is 54 Mbps and 11 Mbps for

IEEE 802.11b). Auto Rate Fallback (ARF) [15] was the first commercial implementation

that exploited multi-rate capability in IEEE 802.11. In ARF, senders use the error rates of

previous transmissions to adaptively select future (attempted) transmission rates. That is,

after a number of consecutive successful transmissions, the sender modifies its modulation


0.5 1 1.5 2!95

!90

!85

Rec

eive

d Po

wer

(dbm

)

Time (sec)0.5 1 1.5 2

!6

!4

!2

0

2

4

6

Rat

e (M

bps)

Figure 1.7: Illustration of channel condition variation

scheme to increase transmission rate. Similarly after consecutive losses it reduces the data

rate. Consequently, if a mobile user has (for example) a perpetually high-quality channel, the

user will eventually transmit at higher data rates. Receiver Based Auto Rate (RBAR) was

RTS

CTS

DATA

ACK

NAV (RTS)

NAV (CTS)

Source

Destination

Others

Delayed Medium Access Channel Access with Backoff

SIFS SIFS SIFS SIFS

RSH

Figure 1.8: IEEE 802.11 with RBAR enhancement

proposed in [12], in which the key idea is for receivers to control the transmission rate. To

guarantee that all stations receive the messages (RTS,CTS and ACK) error free, all messages

in IEEE 802.11 must be sent at the base rate. Using the received RTS message, receiver

determines the maximum possible transmission rate for a given acceptable bit error rate.

The receiver sends back the calculated rate to the tranmitter by adding it into a special field

of the CTS message. Note that all other nodes overhearing this message are also informed of

the modified transmission rate. This message is termed reservation-sub-header (RSH) and


is inserted preceding data transfer as illustrated in Figure 1.8. With the RSH message, over-

hearing nodes can modify their NAV values to the new potentially decreased transmission

time. The explicit messaging in RBAR causes a quick adaptation to channel variations and

extracts significant throughput gains as compared to ARF.

Although ARF and RBAR increase the data rate, at each access of channel they tend

to send a single packet. Since the packet length is fixed, a channel access with lower trans-

mission rate keeps the channel for a longer time in compare with higher data rate packet

transmission. The key OAR mechanism is to allow a flow to keep the channel for multiple

packet transmission (instead of for a single packet) when channel quality is good and higher

data rate is feasible. In OAR, the same amount of time is granted to a sender as if the sender

is transmitting at the base rate. For example, if the base rate is 2 Mbps and the channel

condition is measured such that transmission at 11 Mbps is feasible, the sender is granted a

channel access time to send b11/2c = 5 packets.

Note that all three extensions of IEEE 802.11 protocol are examples of channel adaptation

developed in Section 1.3.3. With the difference that optimum power allocation is not included

and transmitted power is kept constant and only adaptive rate allocation is considered. Next

section gives insight on how OAR can be implemented and added to IEEE 802.11 [31].

1.4.3 OAR Protocol

In order to allow the sender to hold the channel for multiple packet transmission, the fragmen-

tation mechanism of IEEE 802.11 can be exploited. The fragmentation mechanism defined

as part of the IEEE 802.11 standard and mandated for implementation provides a simple

and practical way for nodes to hold the channel for multiple packets when high data rates are

measured. In particular, as in RBAR, the receiver indicates the available physical-layer rate

via the RTS/CTS messages. If the data rate is above the base rate, the more fragments flag

in frame control field of MAC header is set by the sender until btransmission rate / base ratecpackets are transmitted. The duration field carried by the data and the subsequent ACK is

also updated to indicate that the medium will be busy until the end of next data packet.


Thus, as described above, each data packet and ACK serve as a virtual RTS/CTS so that

no additional RTS/CTS frames need to be generated after the initial RTS/CTS handshake.

The sender must also set the fragment number subfield in the sequence control field of the

MAC header to be 0. This prevents the receiver from treating the data packet as a part of

an actual fragmented packet.

To illustrate the protocol time-line consider the following example in which node 1 has

a good channel (11 Mbps) and node 2 has a poor channel (5.5 Mbps). As depicted in

Figure 1.9, in one case node 1 uses the OAR modification and in another case uses RBAR.

Using OAR, node 1 retains channel access and sends four more packets without any channel

contention. Whereas, RBAR goes into contention immediately after the transmission of

node 1 is completed. The backoff counter for node 2 was frozen while node 1 was transmitting,

and node 1 picks a new backoff counter after finishing its transmission. Thus, with high

probability, node 2 gets access to the channel and sends its data at 5.5 Mbps. Thus, RBAR

loses in throughput due to extra contention after every packet in addition to not capitalizing

fully when good channels are encountered.

RTS

CTS

NODE 1(PKT 0) ACK 0OAR

RBAR

ACK 1 ACK 2

RTS

CTS

NODE 1i

NODE 1(PKT 1) NODE 1(PKT 2)

ACK CTSRTS NODE 2i ACK CTSRTS NODE 1i ACK

ACK 4NODE 1(PKT 4)ACK 3NODE 1(PKT 3)

RANDOMBACKOFF TIME

RANDOMBACKOFF TIME

11 Mbps

11 Mbps 11 Mbps 11 Mbps 11 Mbps 11 Mbps

11 Mbps5.5 Mbps

Figure 1.9: Illustration of OAR and RBAR Time-lines for a two node system. Node 1 is ina better channel state than node 2 (11 versus 5.5 Mbps).

Figure 1.10 shows the throughput gain of OAR over RBAR for different number of flows.

Observe that in all cases, OAR results in significant throughput gains as compared to RBAR

in the range of 42% to 56%. OAR extracts this gain by holding the channel when it is good

to the longest extent possible subject to maintaining the base-rate time shares. Moreover,

observe that as the number of flows increases, the throughput gain of OAR as compared

to RBAR also increases. This increase is due to two factors. First, with a higher number

of contending flows, the fraction of time that a flow with a good channel is accessing the

medium is higher, resulting in increasing gains. That is, since flows send a single packet at

the base rate, but up to 5 consecutive packets at higher rates, additional users provide more


0 5 10 15 2020

25

30

35

40

45

50

55

60

Thro

ughp

ut G

ain

(%)

Number of Flows

Figure 1.10: OAR throughput gain as a function of the number of flows.

opportunities for a flow to be in a good-channel state thereby extracting further gains from

opportunistic scheduling. Second, OAR reduces the contention overhead since nodes with a

good channel exploit the channel for transmission of additional packets. Since IEEE 802.11

as well as RBAR have increasing contention times for an increasing number of nodes, OAR

extracts increased throughput gains with a larger number of nodes by decreasing contention

time.

Finally, note that for both RBAR and OAR, the throughput gains as compared to base-

rate IEEE 802.11 are significant. For example, for 10 flows, RBAR obtains a gain of 230%

throughput as compared to IEEE 802.11, and OAR obtains an additional throughput gain

of 51% as compared to RBAR, or 398% above IEEE 802.11.

1.5 Spatio-Temporal-Spectral Opportunism in Ad hoc Networks

In many wireless systems, the available spectrum is more than what is used, thus the system

has multiple channels (frequency bands) available for transmission. If the channel condition

of all the frequency bands are known at the transmitter, then sender can choose the channel

with best quality in order to maximize its throughput. However, knowledge of channel

qualities is not free and there is a cost (requires time and power) associated to channel

1.5. SPATIO-TEMPORAL-SPECTRAL OPPORTUNISM IN AD HOC NETWORKS 29

measurement.

The key idea of Multi-band Opportunistic Auto Rate (MOAR) is to allow nodes to find

the band with the best channel quality. The search should be done in an optimal way such

that the net throughput is maximized while the measurement overhead is kept as low as

possible.

1.5.1 MOAR Protocol

In this section we describe how MOAR employs a band skipping technique within the IEEE

802.11 framework.2 All nodes initially reside on a single common frequency band, known as

the home band. DATA transmission is preceded by the sender transmitting an RTS packet

to the receiver on the home band. On reception of the RTS frame, the receiver makes

the decision to skip by comparing the measured SNR to a channel skip threshold.3 If the

measured SNR is low, the sender and receiver skip to a new channel in search of a better

quality channel, whereas if the measured SNR is high, data is transferred on the current

frequency channel as in the OAR protocol, in which nodes transfer multiple back-to-back

packets in proportion to their channel quality.

On making the decision to skip, the receiver selects a band to skip to and piggy-backs this

channel on the CTS packet. After transmitting the CTS frame, the receiver immediately

skips to the new frequency channel and waits for another RTS from the receiver for a time

equal to the CTS timeout value as mandated by the IEEE 802.11 standard. Since we assume

that in a realistic setting channel conditions on other frequency channels are unknown, the

band to which the receiver decides to skip is selected randomly among the available frequency

bands. Yet, if information regarding channel conditions or interference on some other band

is known (e.g, in a wireless LAN scenario where the Access Point (AP) may have information

regarding interference on other bands), the receiver can take that into account to make a

better decision about which band to skip to. However, for the purpose of this discussion we

2Although our discussion of MOAR is within the context of the RTS/CTS mechanism within the DCF mode of IEEE 802.11,the concepts are equally applicable to other RTS/CTS based protocols such as SRMA [36] and FAMA [8].

3A reasonably accurate estimate of the received SNR can be made from physical-layer analysis of the PHY layer preambleto each packet.


do not require the existence of such information.

If after skipping to a new band, the receiver does not receive another RTS from the sender

within a CTS timeout period, the receiver node switches back to the home band and starts

contending for channel access as mandated by the IEEE 802.11 standard.

Once the sender receives confirmation of the choice of band to skip to from the receiver (via

a CTS frame), it immediately skips to that band. Note that the time elapsed for switching

channels is ∼1µs [7] and has negligible overhead. After skipping to the selected channel, the

transmitter and receiver renegotiate the data rate via another RTS/CTS exchange which

also serves the dual purpose of measuring the channel. In case the channel quality on the

new band is measured to be below the skip threshold, the sender-receiver pair can choose to

skip again in search of a better quality channel.

Since RTS/CTS exchange prior to any channel skip is done at the base rate on the home

band, all nodes within radio range of the receiver and the transmitter can also decode these

packets. However, some nodes (including nodes within radio range of the sender but outside

the radio range of the receiver) may be unable to hear the CTS packet and are unable

to detect whether a decision to skip bands was made or not. Moreover, even though nodes

within radio range of the receiver can correctly decode a CTS packet and infer that a decision

to skip has been made, they are unable to set a correct defer time since it is not known a

priori how many times the sender-receiver pair may skip in search of a better quality channel.

This can lead to problems similar to the hidden terminal problem [2].

To solve the problem mentioned above, all MOAR nodes upon reception of an RTS/CTS

packet defer (via the Network Allocation vector, NAV) for a fixed amount of time correspond-

ing to a maximum time, Dskip, necessary for the transmitter and receiver to skip (multiple

times, if required) to a better quality channel and finish the DATA/ACK transmission. Dskip

is given by

Dskip = K · Toverhead + TD, (1.28)

where, K is the maximum number of allowed channel skips, Toverhead is the time taken for

RTS/CTS exchange at base rate, including all the defer timers (EIFS, SIFS, DIFS etc) as

1.5. SPATIO-TEMPORAL-SPECTRAL OPPORTUNISM IN AD HOC NETWORKS 31

mandated by the IEEE 802.11 standard. The time period TD represents the time to send

data packet at the base rate.

We refer to Dskip as a temporary reservation, to denote the fact that the reservation is not

an actual reservation but represents a maximal amount of reservation time. A temporary

reservation serves to inform the neighboring nodes that a reservation has been requested

but the duration of the reservation is not known. Any node that receives the temporary

reservation is required to treat it the same as an actual reservation with regard to later

transmission requests; that is if a node overhears a temporary reservation it must update its

NAV so that any later requests it receives that would conflict with the temporary reservation

must be denied. Thus the temporary reservation serves as a placeholder until either a new

reservation is received or is canceled. If the sender-receiver pair decide not to skip bands then

they can proceed with the DATA/ACK exchange on the home band as dictated by OAR in

which case other nodes can replace the temporary reservation with the exact reservation, as

carried in the DATA/ACK packets.

Once the transmitter and the receiver conclude the DATA/ACK transmission by skipping

to one or more bands, they return to the home band. The ACK for the final packet (recall

in OAR, nodes can send multiple back-to-back packets) is sent in the home band at base

rate by the sender, and the sender rebroadcasts the same ACK. The two-way ACK in the

home-channel is necessary to ensure that all the nodes within the range of either the sender

and/or the receiver can correctly infer the end of channel skipping and cancel the temporary

reservation timer. In case a node is unable to hear either the updated reservation or the

DATA/ACK transmission signalling the end of the temporary reservation, it would be able

to contend for the channel again after the temporary reservation has expired.

1.5.2 Performance Study of MOAR

Here we consider random topologies representative of a wireless LAN and consider a scenario

where the link distance is uniformly distributed in a circular area with diameter 250 m. We

fix the Ricean fading parameter to K=4 and also set the size of the estimation window to


60 packets, as discussed in the previous section. Figure 1.11 shows the average throughput

gain of MOAR over OAR (computed on per-flow basis and then averaged over flows) as

well as the 95% confidence interval values of the percentage gain for each number of flows.

The curve labeled “Look-ahead” represents the genie-aided protocol in which channel state

information for all the 11 bands is known a priori and thus flows need to skip at a maximum

of one time to the band with known higher rate than the present band. This serves as an

upper bound to the gain that MOAR can extract over OAR. We also implement the optimal

skipping rule and plot the throughput gains of MOAR with optimal skipping over OAR.

The opportunistic gain that MOAR can extract is dependent upon the distance between

0

5

10

15

20

25

30

35

2 4 6 8 10

Thro

ughp

ut g

ain

of M

OAR

ove

r OAR

(%)

Number of Flows

MOARLook Ahead

Figure 1.11: Throughput gain of MOAR for random fully connected topologies

the sender and receiver of a flow. For a given random topology, some of the flows are

located in a region where the opportunistic gain obtained by skipping bands is not significant.

These nodes, besides contributing little to the net overall gain that MOAR can obtain,

actually reduce the opportunistic gain for better located nodes. The reason for this can be

attributed to the random nature of the MAC. Whenever nodes with lower opportunistic gain

access the medium, nodes which are better located to exploit the opportunistic gain through

band skipping defer medium access. Thus, the net opportunistic gain that can be obtained

by exploiting channel diversity is reduced. However, on average MOAR still outperforms

OAR by 14-24%. Also note that the gain of MOAR with optimal skipping is very close

1.6. CONCLUSIONS 33

to the maximum gain achievable if the channel condition on all the 11 bands is known a

priori. Thus, in realistic systems where channel state information on other channels may

be unavailable, the optimal skipping rule can still enable MOAR to capture most of the

performance gains available via opportunistic skipping.

1.6 Conclusions

In this chapter, we discussed the general ideas of adaptation to exploit the inherent time-

variability of sources and channels in wireless networks. The significant gain in all cases

makes opportunistic algorithms as default candidates for any new design of high-performance

network elements.

It is necessary to say that the adaptive algorithms are not limited to what is mentioned

in this chapter. For example in [39, 19] an adaptive beamforming scheme is investigated.

Beamforming algorithms, matches the phase of the input signal to the phase of the channel

such that the received signals (in a multiple antenna system) are combined constructively.

Opportunism can be exploited in scheduling in many ways. In this chapter we talked about

source scheduling of a single queue. Opportunistic scheduler can be extended to a multiuser

scheduler [24, 21], in addition to the best user scheduling adding new spatial degrees of

freedom even in single-antenna systems, often referred to as multiuser diversity [11, 41].

In a multiple antenna system another way of exploiting the spatial degrees of freedom is

by antenna selection in which the transmitter only uses one or a subset of possible transmit

antennas [25, 33]. On higher networks layers, opportunistic routing can be done in which

the best route or a subset of routes among all possible routes is chosen [4, 17]. We believe

that there are numerous many other ways that one can uses the information about source

and channel, and adapt the transmission scheme in a beneficial way.


References

[1] Dimitri P. Bertsekas and Robert Gallager. Data Networks. Prentice Hall, 1992.[2] V. Bharghavan, S. Demers, S. Shenker, and L. Zhang. MACAW: A media access protocol

for wireless LANs. In Proceedings of ACM SIGCOMM ’94, London, UK, 1994.[3] E. Biglieri, G. Caire, and G. Taricco. Limiting performance of block-fading channels

with multiple antennas. IEEE Trans. Inform. Theory, 47(4):1273–1289, May 2001.[4] C. Cetinkaya and E. Knightly. Opportunistic traffic scheduling over multiple network

paths. IEEE INFOCOM’04, 3:1928–1937, 2004.[5] Thomas M. Cover and Joy A. Thomas. Elements of Information Theory. John Wiley

& Sons Inc., 1991.[6] M. E. Crovella and A. Bestavros. Self-similarity in world wide web traffic: evidence and

possible causes. IEEE/ACM Transacations on Networking, 5(6):835–846, Dec. 1997.[7] R. Garces and J. J. Garcia-Luna-Aceves. Collision avoidance and resolution multiple

access for multichannel wireless networks. In Proceedings of IEEE INFOCOM 2000,pages 595–602, Tel Aviv, Israel, 2000.

[8] J. J. Garcia-Luna-Aceves and C. Fullmer. Floor acquisition multiple access (FAMA) insingle-channel wireless networks. ACM Mobile Networks and Application (MONET),Special issue on Ad Hoc Networks, 4:157–174, 1999.

[9] J. C. Geromel, M. C. De Oliveira, and J. Bernussou. Robust filtering of discrete-timelinear systems with parameter dependent lyapunov functions. SIAM Journal on Controland Optimization, 41(3):700–711, 2002.

[10] A. J. Goldsmith and P. P. Varaiya. Capacity of fading channels with channel sideinformation. IEEE Trans. Info. Th., 43(6):1986–92, Nov. 1997.

[11] M. Grossglauser and D. N. C. Tse. Mobility increases the capacity of adhoc wirelessnetworks. IEEE Transactions on Networking, 10(4):477–486, Aug. 2002.

[12] G. Holland, N. Vaidya, and P. Bahl. A rate-adaptive MAC protocol for multi-hopwireless networks. In Proceedings of ACM MOBICOM’01, Rome, Italy, 2001.

[13] TIA/EIA IS-856. ”CDMA 2000: High rate packet data air interface specification”. Std,November 2000.

[14] S. K. Jayaweera and H. V. Poor. Capacity of multiple-antenna system with both receiverand transmitter channel state information. IEEE Trans. Info. Theory, 49(10):2697–2709, Oct. 2003.

[15] A. Kamerman and L. Monteban. WaveLAN II: A high-performance wireless LAN forthe unlicensed band. Bell Labs Technical Journal, pages 118–133, Summer 1997.

[16] M. A. Khojastepour and A. Sabharwal. Delay-constrained scheduling: Power efficiency,filter design and bounds. IEEE INFOCOM, 2004.

[17] A. Khoshnevis and A. Sabharwal. Network channel estimation in cooperative wirelessnetworks. Canadian Workshop on Information Theory, May 2003.

[18] A. Khoshnevis and A. Sabharwal. On the asymptoti performance of multiple antennachannels with fast channel feedback. submitted to IEEE Trans. on Inform. Theory,2005.

[19] I-M. Kim, S-C Hong, S. S Ghassemzadeh, and V. Tarokh. Opportunistic beamformingbased on multiple weighting vectors. IEEE Transaction on Wireless Communications,4(6):2683–2687, Nov. 2005.

[20] R. Knopp and P. A. Humblet. Information capacity and power control in single-cellmultiuser communications. In Proc. ICC, pages 331–335, June 1995.

[21] C. Li and X. Wang. Adaptive opportunistic fair scheduling over multiuser spatial chan-nels. IEEE Transaction on Cp,,imocatopms, 53(10):1708–1717, Oct. 2005.

[22] Q. Liang. Ad hoc wireless network traffic: Self-similarty and forecasting. IEEE Com-munications Letters, 6(7):297–299, July 2002.

[23] L. Lin, R. D. Yates, and P. Spasojevic. Adaptive transmission with discrete code rates

1.6. CONCLUSIONS 35

and power levels. IEEE Trans. on Communications, 51(12):2115–2125, Dec. 2003.[24] X. Liu, E. K. P. Chong, and N. B. shroff. Opportunistic transmission scheduling with

resource-sharing constraints in wireless networks. IEEE Journal on Selected Areas inCommunicaitons, 19(10):2053–2064, Oct. 2001.

[25] Y. Liu and E. Knightly. Opportunistic fair scheduling over multiple wireless channels.IEEE INFOCOM’03, 2:1106–1115, 30 March-3 April 2003.

[26] S. O. R. Moheimani, A. V. Savkin, and I. R. Petersen. Robust filtering , prediction,smoothing and observability of uncertain systems. IEEE Transactions on Circuits andSystems, 45(4):446–457, 1998.

[27] B. O’Hara and A. Petrick. IEEE 802.11 Handbook, A Designer’s Companion. IEEEPress, 1999.

[28] L. H. Ozarow, S. Shamai, and A. D. Wyner. Information theoretic considerations forcellular mobile radio. IEEE Trans. Info. Th., 43(2):359–378, May 1994.

[29] D. Rajan, A. Sabharwal, and B. Aazhang. Delay-bounded packet scheduling of burstytraffic over wireless channels. IEEE Trans. Info. Th., 50(1):125–144, January 2004.

[30] A. Sabharwal, A. Khoshnevis, and E. W. Knightly. Opportunistic spectral usage:Bounds and a multip-band csma/ca protocol. Submitted to IEEE/ACM Transacationson Networking, 2005.

[31] B. Sadeghi, V. Kanodia, A. Sabharwal, and E. Knightly. OAR: An opportunistic auto-rate media access protocol for ad hoc networks. To appear in ACM/Baltzer MobileNetworks and Applications (MONET): Special Issue on Selected Papers from MobiCom2002, 2003.

[32] Linn I. Sennott. Stochastic Dynamic Programming and the control of Queueing Systems.John Wiley and Sons, Inc., 1999.

[33] N. Sharma and L. H. Ozarow. A study of opportunism for multiple-antenna systems.IEEE Transaction on Information Theory, 51(5):1804–1814, May 2005.

[34] D. Slepian. On bandwidth. Proc. IEEE, 64(3):292–300, March 1976.[35] I. E. Telatar. Capacity of multi-antenna Gaussian channels. Technical report, AT&T

Bell Labs, 1995. (Appeared in Eur. Trans. Tel., vol. 10, no. 6, pp. 585–595, 1999).[36] F. A. Tobagi and L. Kleinrock. Packet switching in radio channels: Part III - polling

and (dynamic) split-channel reservation multiple access. IEEE Transactions on Com-munications, 24(8), 1976.

[37] D. Tse and P. Viswanath. Fundamentals of Wireless Communications. CambridgeUniversity Press, 2005.

[38] P. Vishwanath, D. Tse, and R. Laroia. Opportunistic beamforming using dumb anten-nas. IEEE Transactions on Information Theory, 48(6):1277–1294, June 2002.

[39] P. Viswanath, D. N. C. Tse, and R. Laroia. Opportunistic beamforming using dumbantennas. IEEE Transaction on Information Theory, 48(6):1277–1294, June 2002.

[40] W. Willinger, M. S. Taqqu, r. Sherman, and D. V. Wilson. Self-similarity through high-variability: statistical analysis of ethernet LAN traffic at the source level. IEEE/ACMTransacations on Networking, 5(1):71–86, Feb. 1997.

[41] D. Wu and R. Negi. Utilizing multiuser diversity for efficient support of quality ofservice over a fading channel. IEEE Transaction on Vehicular Technology, 55(3):1298–1206, May 2005.

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